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Method for fitting power function type stage-discharge relation

A power function and water level technology, applied in complex mathematical operations, etc., can solve problems such as dissatisfaction, and achieve easy-to-implement and good results

Inactive Publication Date: 2012-09-26
JIANGSU VOCATIONAL INST OF ARCHITECTURAL TECH
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Problems solved by technology

[0029] In order to overcome the traditional method for fitting the power function type water level and flow relationship, the required fitting parameters do not satisfy the dependent variable, that is, the residual sum of squares of the flow is the minimum, and the resulting regression line is not the defect of the best fitting curve. The present invention adopts the Gauss-Newton method , fitting power function water level and flow relationship

Method used

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  • Method for fitting power function type stage-discharge relation
  • Method for fitting power function type stage-discharge relation
  • Method for fitting power function type stage-discharge relation

Examples

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example 1

[0051] Example 1 shows that the Gauss-Newton method is significantly better than the traditional method, and the fitting accuracy is significantly improved; the Gauss-Newton method is the same as the literature [5] method, and is better than the literature [6]. [5], literature [6] method is simple.

example 2

[0060] Example 2 shows that the Gauss-Newton method is significantly better than the traditional method, and the fitting accuracy is significantly improved.

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Abstract

The invention relates to a method for fitting a power function type stage-discharge relation, and belongs to the technical field of hydrology and water resources. The method includes utilizing a larger group of relation values and a smaller group of relation values in n groups of relation values to determine initial values theta (0)=[beta 0(0), beta (0)]' of parameters to be estimated in a power function type stage-discharge relation formula according to a stage-discharge relation value (Ze1, Q1) to be fit in a certain hydrometric station, or solving a nonlinear regression coefficient as initial values of the parameters beta 0 and beta to be estimated by a traditional method of converting nonlinear regression to linear regression; and determining regression coefficients beta 0 and beta by a Gauss-Newton method. An i ranges from 1 to n. The stage-discharge relation is one of important contents for reorganizing hydrologic data, and is one of important references for water-conservancy and water-power engineering planning programming, hydrological forecasting and reservoir regulation.

Description

1. Technical field [0001] The invention belongs to the technical field of hydrology and water resources. The relationship between water level and flow is one of the important contents of hydrological data compilation; it is one of the important basis for planning and design of water conservancy and hydropower projects, hydrological forecasting and reservoir scheduling. 2. Background technology [0002] The relationship between water level and flow is often selected as a power function type [1] : [0003] Q = β 0 ( Z - Z 0 ) β = β 0 Z e β - - - ( 1 ) [0004] In the formula, Q——flow rate, m 3 / s; Z—wate...

Claims

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Application Information

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IPC IPC(8): G06F17/10
Inventor 张子贤
Owner JIANGSU VOCATIONAL INST OF ARCHITECTURAL TECH
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